If you wish to do this hike on your own go to "npm.cpami.gov.tw/en". Choose "Trails, Campgrounds and Bed Avaiability" and choose "Yushan Cabin and Campground Availability" and choose "Paiyun Lodge". You will see the calendar. If you are a foreigner they reserve 24 spaces from Sunday to Thursday and when you look at the dates the last item is "Advanced Application" so if this number is under 24 you will get a slot. You can apply 4 months to 35 days prior to your hiking date if choosing the 24 space allotment.
Then go to "Online Application" and choose "Yushan National Park". Check the box and agree. Then choose the "Paiyun Lodge Advanced Application". Choose your group name and "Yushan Trails" and "2 Days". Then hiking days "2". Then your start date.
Your route will be "Tataka Trail Head, Paiyun Lodge, End a day". The next day will be "Mt Jade Main Peak, Paiyun Lodge, Tataka Trail Head, End a day". You can add the Front Peak, West Peak and North Peak. I highly recommend the North Peak but you don't need to put it on your route. Choose how many in your group. Answer the required questions and the other boxes I left blank.
Then you need to fill out the "Applicant/Agent", "Leader", "Member", "Emergency Coordinator". While filling this out the emergency contact needs a local phone number. No problem- use your hotel and I used my sister's name even with the hotel local phone.
You need to submit the application during working hours and after you submit the application you will get an email confirming the application and shortly after that another one in English and everything will be explanatory. We were allowed to pay for the Paiyun Lodge(480 per bed) and get our national park permits and mountain police permits on the day of the hike.
I also asked them to book the Dongpu Hostel(300 per bed) which is close to the trailhead. There are buses from Alishan to Sun Moon Lake leaving at 13:00 and 14:00 costing 70 and arriving 1/2 hour later. Tell the driver to drop you at Dongpu Lodge. Surprisingly Dongpu Hostel wouldn't let us store our bags we didn't take for the hike but the police stored them.
We took 1 hour and 15 minutes from the Paiyun Lodge to the Main Peak and added 2 1/2 hours roundtrip to the North Peak but were quite fast. We were the only people in the lodge who didn't go for sunrise and were happy about that because if you go for sunrise the peak will be packed and the trail slow when you get to the chains. We started the day at 5am and managed to catch the 13:30(also 14:30) bus on to Sun Moon Lake. If you want to go slow or add more peaks think about booking Dongpu Lodge for the day you descend. If you want to reserve dinner and breakfast(2am I think) ask via email- we brought our own food but were the only ones it seemed.